Loci Flashcards

All 6 cards in this deck

What is a locus?

The set of all points that satisfy a given rule or condition.

What is the locus of points a fixed distance from a fixed point?

A circle with that radius, centred on the point.

What is the locus of points a fixed distance from a line segment?

Two parallel lines that distance either side, joined by a semicircle of that radius at each end (a 'racetrack' shape).

What is the locus of points equidistant from two points $A$ and $B$?

The perpendicular bisector of $AB$.

What is the locus of points equidistant from two intersecting lines?

The bisector of the angle between the two lines.

What are the steps to shade a region satisfying two loci conditions on a scale diagram?
e.g. less than $4$ cm from $A$ and nearer to $B$ than to $C$

1. Construct each boundary: a circle of radius $4$ cm centred on $A$, and the perpendicular bisector of $BC$.
2. Decide which side of each boundary fits the condition (inside the circle; the $B$ side of the bisector).
3. Shade only the overlap of those regions.